Answer:
Part a) [tex]y=6,000(1.066^x)[/tex]
Part b) [tex]13,772\ people[/tex]
Step-by-step explanation:
Part a) Use the exponential growth model to write an equation that estimates the population t years after 2010
we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
x ---> the number of years since 2010
y ---> the population of a town
a is the initial value or y-intercept
b is the base of the exponential function
r is the rate of change
b=(1+r)
In this problem we have
[tex]a=6,000\ people[/tex]
[tex]r=6.6\%=6.6/100=0.066[/tex]
[tex]b=1+r=1+0.066=1.066[/tex]
substitute
[tex]y=6,000(1.066^x)[/tex]
Part b) Estimate the population of the town in 2023.
we know that
2023-2010=13 years
so
For x=13 years
substitute in the exponential equation and solve for y
[tex]y=6,000(1.066^13)=13,772\ people[/tex]
